Three forms of localized solutions of the quintic complex Ginzburg-Landau equation

We report numerical observation of two new forms of stable localized solutions of the quintic complex Ginzburg-Landau equation. The first form is a stationary sere-velocity solution, which consists of two motionless fronts and a source between them. We call this structure the ''composite'' pulse. We show that in some range of parameters, a composite pulse can coexist with a plain pulse solution. At the boundary of their region of existence in the parameter space, composite pulses exhibit a complicated behavior, which includes periodical dynamics and transition into another new form of localized solutions, namely, uniformly translating, or moving pulses. A careful study shows that the moving pulses have an even wider range of existence than the composite pulses. The interactions between different combinations of moving and stationary pulses are also studied. A qualitative explanation of the observed structures is proposed.